Golfers have a swing frequency associated with the swing of each golf club in a set. The golfer's swing frequency is inversely related to the time of a particular portion of the golfer's normal swing of a club. When the golfer begins his downward swing, he raises the club above his head and then he pulls his arms downwardly toward the ball, thereby accelerating the club. As the downward swing begins, the club flexes backwardly, due to the inertia of the club head tending to remain in place, thereby storing potential energy in the bent club shaft. When the acceleration of the club head reaches a maximum and begins to decrease, the club shaft begins to flex forward and straighten out. This motion is similar to a pendulum passing through its lowest point. The club head has maximum velocity and zero acceleration with respect to the axis of its grip when the shaft has sprung from bent and is passing through the point of its oscillation cycle in which the club shaft is straight. At ball impact, the club head velocity is the sum of its velocity with respect to the grip axis plus the velocity from the motion of the grip axis itself moving approximately circularly in the golfer's hands. Preferably, the club shaft is straight at ball impact, so as to impart maximum momentum to the ball as a result of the club head velocity being maximum when the shaft is straight.
Each particular golf club has a natural frequency at which it will oscillate if it is held at the grip end, bent and released. This is the frequency at which the above described oscillation occurs. It is desirable to match a golfer's swing frequency to the natural frequency of each club in his set so that at ball impact each club shaft is straight.
The swing frequency phenomenon is explained more fully in U.S. Pat. Nos. 5,351,952, 5,441,256 and 5,478,073 to Hackman. These applications and patent describe how swing frequency can be measured. The time that elapses between the time at which club head acceleration is at a maximum and the time of ball impact (at which time acceleration takes a characteristic plunge to negative acceleration) is called swing time, t. Swing time is the time interval in the golfer's swing during which it is desired that approximately one-fourth of an oscillation cycle of the golfer's club occurs to make the club shaft straight at ball impact. It must be assumed that the time from when the club begins to straighten out (at maximum acceleration) until the club shaft is straight (at acceleration of zero) is approximately one-fourth of an oscillation cycle of the golf club. The swing frequency therefore equals one-fourth cycle divided by the amount of time it takes for the club shaft to straighten--which is the swing time, t : EQU frequency=1/(4t)tm (EQUATION 1).
Since a person swinging a golf club does not exert on the club a perfectly sinusoidal driving force, a correction factor, k, is necessary to accommodate the imperfections. The above equation then becomes EQU frequency=k/(4t) tm (EQUATION 2).
Swing frequency can be obtained by measuring the swing time, t from maximum acceleration until ball impact and inserting that time quantity into Equation 1, or Equation 2 if k has been determined.
Currently, clubs must be custom made in order to exactly match a golf club to a golfer's swing. One type of custom matching invention is shown in U.S. Pat. No. 4,122,593 to Braly. Custom making golf clubs involves measuring the swing frequency of the golfer for each particular club length, cutting a club shaft to a particular length while maintaining the desired natural frequency, and assembling the club from multiple parts, including the shaft. This method is labor intensive and it is difficult in this process to correctly cut the club shaft to the length which will give it the desired final frequency. Furthermore, a significant amount of time elapses between the initial measuring of the golfer's swing and completion of the custom made set of clubs. This waiting period adds to the disadvantage of this relatively expensive process.
The other method currently used to match a golfer to a golf club is somewhat inaccurate. This method involves the golfer choosing which one of four stiffness categories he or she wants the set of clubs to have. The stiffness categories are normally denominated, in order from most flexible to stiffest, LADIES, REGULAR, STIFF and EXTRA STIFF. Once the golfer determines which category suits him or her best, one club of each type (e.g. iron, wood) is selected from that chosen stiffness category to make up a set.
The reason this method is inaccurate is that each club in each category may vary widely in natural frequency from every other club in that same category. For example, a person comparing two nine iron, regular stiffness clubs may find that one differs in natural frequency of oscillation from the other by as much as 10 or 20 cycles per minute. A golfer may swing a regular stiffness 9 iron sample club and prefer the "feel" of it. The golfer may order one expecting a similar "feel", but get a club having a frequency varying substantially from the club he had swung.
Most golfers'swing frequencies vary between five cycles per minute and fifteen cycles per minute from swing to swing. Therefore, it is desirable to match the golfer's swing frequency to the natural frequency of a particular club within four cycles per minute. The time from measuring the golfer's swing frequency until receipt by the golfer of the clubs should be very low and the cost, as compared to custom fitting of clubs, should be low.